Column generation (CG) is a powerful technique for solving optimization problems that involve a large number of variables or columns. This technique begins by solving a smaller problem with a subset of columns and gradually generates additional columns as needed. However, the generation of columns often requires solving difficult subproblems repeatedly, which can be a bottleneck for CG. To address this challenge, we propose a novel method called machine learning enhanced ant colony optimization (MLACO), to efficiently generate multiple high-quality columns from a subproblem. Specifically, we train a ML model to predict the optimal solution of a subproblem, and then integrate this ML prediction into the probabilistic model of ACO to sample multiple high-quality columns. Our experimental results on the bin packing problem with conflicts show that the MLACO method significantly improves the performance of CG compared to several state-of-the-art methods. Furthermore, when our method is incorporated into a Branch-and-Price method, it leads to a significant reduction in solution time.

A data marketplace is an online venue that brings data owners, data brokers, and data consumers together and facilitates commoditisation of data amongst them. Data pricing, as a key function of a data marketplace, demands quantifying the monetary value of data. A considerable number of studies on data pricing can be found in literature. This paper attempts to comprehensively review the state-of-the-art on existing data pricing studies to provide a general understanding of this emerging research area. Our key contribution lies in a new taxonomy of data pricing studies that unifies different attributes determining data prices. The basis of our framework categorises these studies by the kind of market structure, be it sell-side, buy-side, or two-sided. Then in a sell-side market, the studies are further divided by query type, which defines the way a data consumer accesses data, while in a buy-side market, the studies are divided according to privacy notion, which defines the way to quantify privacy of data owners. In a two-sided market, both privacy notion and query type are used as criteria. We systematically examine the studies falling into each category in our taxonomy. Lastly, we discuss gaps within the existing research and define future research directions.

Column Generation (CG) is an effective method for solving large-scale optimization problems. CG starts by solving a sub-problem with a subset of columns (i.e., variables) and gradually includes new columns that can improve the solution of the current subproblem. The new columns are generated as needed by repeatedly solving a pricing problem, which is often NP-hard and is a bottleneck of the CG approach. To tackle this, we propose a Machine-Learning-based Pricing Heuristic (MLPH)that can generate many high-quality columns efficiently. In each iteration of CG, our MLPH leverages an ML model to predict the optimal solution of the pricing problem, which is then used to guide a sampling method to efficiently generate multiple high-quality columns. Using the graph coloring problem, we empirically show that MLPH significantly enhancesCG as compared to six state-of-the-art methods, and the improvement in CG can lead to substantially better performance of the branch-and-price exact method.